Existence of Density Functionals for Excited States and Resonances

TL;DR

This paper demonstrates that density functionals exist for all bound states, including excited states and resonances, in finite fermionic systems, extending the foundational framework of density functional theory.

Contribution

It establishes the existence of density functionals for excited states and resonances, including cases with degeneracies and complex scaling techniques.

Findings

Density functionals exist for all bound states of finite fermionic systems.

Degeneracies can be lifted using a pseudo-Zeeman effect.

Resonances regularized by complex scaling also admit density functionals.

Abstract

We show how every bound state of a finite system of identical fermions, whether a ground state or an excited one, defines a density functional. Degeneracies created by a symmetry group can be trivially lifted by a pseudo-Zeeman effect. When complex scaling can be used to regularize a resonance into a square integrable state, a DF also exists.